An Efficient CAI For Teaching/Learning Mathematics
*Moses E. Ekpenyong and Charles I. Chukwu
Abstract: - Mathematics is virtually at the root of every
field in life. Hence, a proper understanding of Mathematics is fundamental
to success in any of these fields. No matter how good a human teacher
is; he or she could never carry the whole class together at the same time.
Reason being that they are humans. The computer has come to every teacher's
aid. It never gets tired of explaining concepts neither does it get tired
of "marking exercises". This is what this paper seeks to achieve.
It helps simplify the learning process by generating randomized exercises
and assisting a teacher in organizing his/her notes of lessons. It also
implements a cutting-edge technique that will not only improve the learner
after a short time of use in a stress-free fashion but also allow for
adaptation possibilities and feedback mechanism. This will gradually lead
to a Mathematical revolution that will positively impact on our nations
Science and Technology development.
Key words: CAI, CAM, PI, CBT, AI, ICT
On absolute summability factors of Walsh-fourier series
Satish Chandra
Abstract: - In this paper we have proved a theorem on absolute summability factors of Walsh-Fourier series which generalizes various known results. However, our theorem is as follows:
Theorem : For Î > 0, the Walsh-Fourier series
is summable
| C, 1 | at a point y = x of the interval [-R,R], | R | < ¥, provided
as t ® 0, d being some fixed positive constant and
Key words and pharases: Absolute summability factors,
Walsh-Fourier series, periodic function Lebesgue integrable.
2000 Mathematics subject classification: 40C05, 40D25, 40EO5, 40FO5 and
40GO5.
Convergence of ( L - a ) uniformly Lipschitz asymptotically quasinonexpansive mapping in uniformly convex Banach space
G.S. Saluja
Abstract: - In this paper, we study convergence of generalized Ishikawa iterative sequence for ( L - a ) uniformly Lipschitz asymptotically quasi-nonexpansive mapping in uniformly convex Banach space.
Key words : Asymptotically quasi-nonexpansive mapping, generalized Ishikawa iteration process, fixed point, ( L - a ) uniformly Lipschitz mapping, uniformly convex Banach space.
2000 Mathematics Subject Classification : Primary 47H09 ; Secondary 47H10.
MHD free convection flow of stratified viscous liquid past porous vertical plate embedded with porous medium
N. P. SINGH*, ASHOK KUMAR, AlAY KUMAR SINGH# and ATUL KUMAR SINGH**
Abstract: - In the present paper unsteady free convection flow of an incompressible, electrically conducting, stratified viscous liquid past a porous vertical plate
subjected to time dependent suction velocity is presented. The flow is considered in porous medium is the presence of magnetic field of uniform strength applied perpendicular to the flow. The technique suggested by Lighthill1 is followed to obtain the solutions of velocity field and temperature distribution. The expressions for skin-friction and rate of heat transfer are also obtained. Effects of various parameters on velocity and temperature distribution are numerically discussed through graphs while the skin-friction and rate of heat transfer are discussed through tables. It is observed that the temperature for mercury remains more stationary in comparison to water and air.
A solution to the Problem of Seepage of Groundwater flow in a Heterogeneous Porous Media on Slopping Bedrock Taking Numerical Approach
Twinkle Patel and M.N. Mehta
Abstract: - The present paper discusses the seepage problem of groundwater in a
Heterogeneous porous media on a sloping bedrock. We have used numerical approach to solve the problem arising into groundwater seepage problem in a
Heterogeneous porous media & here we discussed its nature of free surface, with its graphical representation.
Key words: Numerical Approach, fluid mechanics.
AMS Subject Classification No: 49J40, 65L60, and 76M10.
A finite horizon economic ordering policy for items with deterioration and shortage
Sanjay Jain and Mukesh Kumar
Abstract: - In this paper an inventory model is developed for determining the
economic ordering policy (EOP) for an item, which is required over a finite time period with deterioration, planned shortage and backordering. This model is more general then the model earlier obtained by Goya13. The model is illustrated with a numerical example and calculated various parameters.
Key word : EOP, Deterioration, Shortage, Backorder
AMS subject classification: 90 B 05
MHD free convection flow of viscous fluid past a porous vertical plate through non- omogeneous porous medium with radiation and temperature gradient dependent heat source in slip flow regime
N. P. SINGH*, ASHOK KUMAR, AJAY KUMAR SINGH# and ATUL KUMAR SINGH**
Abstract: - The present paper deals with the analysis of unsteady free convection flow through a porous medium of variable permeability bounded by an infinite porous vertical plate in slip flow regime taking into account the radiation and temperature gradient dependent heat source. The flow is considered under the influence of magnetic field applied normal to the flow. The permeability of the porous medium and the suction velocity at the plate decreases exponentially with time about a constant mean. Approximate solutions for velocity and
temperature fields are obtained using perturbation technique. The expressions for skin-friction and rate of heat transfer are also derived. The results obtained are discussed for cooling case (Gr > 0) of the plate. The effects of various physical parameters, encountered into the problem, on the velocity field are numerically shown through graphs while the effects on skin-friction and rate of heat transfer are numerically discussed through tables.
Existence of smooth epimorphism from a Fuchsian group to the dihedral group
*Buddha Prasad Chetiya and **Chandra Chutia,
Abstract: - In this paper we determine a set of necessary and sufficient conditions for existence of smooth epimorphism from a Fuchsian group G to the dihedral group Dn of order 2n (n ³ 3).
Key words : Fuchsian group, smooth quotient, Riemann surface, automorphism group, Dihedral group.
Inventory model with hypo exponential lifetime having demand as function of selling price and time
K. SRINIVASA RAO1 P.V.G.D. PRASAD REDDY2 and Y. GOPI NATH3
Abstract: - In this paper, we develop and analyze an inventory model for deteriorating items. Here we assume that the lifetime of the commodity is random and follows an additive exponential distribution. We further assume that the demand is a function of time and selling price. Using the differential equations the instantaneous state of inventory is obtained. With suitable cost considerations the total cost function is derived. The optimal ordering and pricing policies are obtained by maximizing the profit rate function. The sensitivity of the model with respect to the parameters is studied. These models are very useful in situations arising at places like, fruit and vegetable markets and food processing industries etc., in which the lifetime of the commodity is the sum of two components, namely, natural lifetime and extended lifetime due to cold storages or chemical treatments. This model also includes the exponential lifetime model as a limiting case.
Key words: Perishability, instantaneous rate of deterioration, backlog demand, ordering quantity.
AMS 1991 Subject Classification: 90B05
Common fixed point theorem for compatible maps in probabilistic metric space
Ramesh Kumar Vats
Abstract: - The aim of this paper is to prove a result in Menger spaces which
generalizes the results of Jachymski1, Kang and Kim3 and Rhoades et al.6 and many other authors illustrating with an example.
Key Words : Compatible maps, Fixed point, Menger space.
Subject classification: (2001) AMS: 47H10, 54H25
Optimum Stratification for Two Sensitive Variables- Ratio Method of Estimation
1M.R. Verma*, J.P. Singh Joorel** and R.K. Agnihotri***
Abstract: - This paper considers the problem of optimum stratification for two
sensitive quantitative variables Yj (j=1,2) when samples from different strata are selected with simple random sampling with replacement (SRSWR) for ratio method of estimation when an auxiliary variable is taken as stratification variable under proportional method of allocation and scrambled response technique is used to collect data on sensitive study variables.
Key words: Sensitive variable, scrambled response, optimum stratification
Pulsatile flow of couple stress fluid through a stenosed porous media under periodic body acceleration
V. P. Rathod and Gopichand T. Pawar
Abstract: - An interesting mathematical model has been proposed to study the pulsatile flow of blood through a stenosed porous media to the narrow tube under the influence of Periodic body acceleration. The importance of the study of the effect of body acceleration on the blood flow has been emphasized. Blood is considered as a couple stress fluid. With the help of finite Hankel and Laplace transforms, analytical expression for axial velocity, flow rate and fluid acceleration have been obtained. The velocity variations with different parameters have been shown graphically. Finally, some biological implications of this theoretical
investigation have been indicated.
Key word : Blood flow, couple stress fluid, body acceleration, stenosed and Porous medium.
Interdependent queueing model with jockeying
K. SRINIVASA RAO1, K.S. SRINIVASA RAO2, P.V.G.D. PRASAD REDDY3 and P. SRINIVASA RAO4
Abstract: - In this paper we introduce an Interdependent Queueing Model with
Instantaneous Jockeying. The system consists of two queues in parallel having infinite capacity with FCFS queue discipline and the number of arrivals and service completions are correlated and follow a bivariate poisson process. The customer strategy here is, if at any time the difference in the number of customers in two queues exceeds unity, the last customer in the longer queue jockeying to the end of the shorter queue and this jockeying is instantaneous, which implies that customers always jockey to the shorter queue. Using the difference differential equations the joint probability distribution of the number of customers in each queue is obtained. The System characteristics of the model are obtained and analyzed. This model is extended to the interdependent queueing model with instantaneous jockeying and customer preference. These models are much useful in performance evaluation of computer communication systems, Satellite
Communication Systems, Railway Reservations, Scheduling reader / writer queues etc.
Key words: Interdependent Queue, Queue Size Distribution, Instantaneous Jockeying, Bivariate Poisson Process.
On matrix summability of jacobi series
SHYAM LAL and HARE KRISHNA NIGAM*
Abstract: - In this paper a new theorem on Matrix Summability of Jacobi series is established. This theorem is a generalization of several known results.
Experimental Study of Knowledge Representation in a Knowledge-Based System (A Case Study of Diagnosis and Therapy of Typhoid Fever)
OBOT, Okure Udo
Abstract: - Knowledge acquisition and representation are two essential necessities of a knowledge-based system. Acquisition is concerned with the collection of knowledge from a domain expert while representation depicts how knowledge is presented by a knowledge engineer to a computer in an understandable form. The duo is therefore very essential in the building of a reservoir of knowledge for use as an expert system. In this paper, the author presents the principles, practice of knowledge acquisition and representation. He then caps it with the acquisition of knowledge for the diagnosis and therapy of typhoid fever. Finally, the acquired knowledge is represented in a computer understandable form using a case based system exhibited by visual basic 6.0 programming language.
Common fixed point theorem in generalized fuzzy metric space
Sangeeta Kulhare, Rajesh Shrivastava* and Manoj Sharma**
Abstract: - Our aim of this paper is to obtain a common fixed point theorem for two self mappings of generalized fuzzy metric space (i.e. S-Fuzzy metric space), Which generalize the recent result of Singh and Chauhan.
Key words : S-Fuzzy metric space, common fixed point.
Steady
MHD boundary layer flow and heat transfer along an infinite hot vertical
porous
moving plate with heat source
Abstract: - Aim of the paper is to investigate steady
boundary layer flow and heat transfer through a viscous incompressible
electrically conducting fluid along an infinite hot vertical porous moving
non-conducting plate in the presence of
constant suction, uniform free stream velocity and heat source. The governing
equations of motion and energy are solved by using the regular perturbation
technique. The velocity and temperature distributions are derived, discussed
numerically and shown through graphs for externally cooling/heating of
the plate. The expressions of skin-friction coefficient and the Nusselt
number at the plate are derived, discussed numerically and their numerical
values for various values of physical parameters for externally cooling/heating
of the plate are presented through Table.
Key words : Steady, MHD, boundary layer, porous, heat
source, skin-friction, Nusselt number.
Fixed point theorem in D-Metric spaces
Devendra Singh Solanki
Abstract: - This paper deals with fixed point theorem with concept of D-Metric space [1 & 2]. In first part some basic definitions, examples and lemma are given. And then some results are obtained in generalized metric space.
Key words : D-Cauchy sequence, Bounded D-metric space
AMS subject classification 47H10.
Unsteady
flow and heat transfer through a rotating porous medium in the presence
of heat source and variable free stream
P. R. Sharma and Rachna Katta
Abstract: - Unsteady flow of a viscous incompressible
fluid through a rotating
porous medium with variable surface temperature, variable free stream
in the presence of heat source is investigated. The governing equations
of motion and energy are solved by using complex function. The axial and
transverse components of velocity and temperature distribution are derived,
discussed and shown through graphs. The expressions of skin-friction coefficient
along X*- and Z*- directions and Nusselt number at the surface are derived,
discussed and their numerical values for various values of physical parameters
are presented through Tables l and 2, respectively.
Key words : Unsteady, heat transfer, rotating porous
medium, source, Skin-friction and Nusselt number.
Common Fixed Points of Lipschitz Type Mapping Pairs
Sanjay Kumar
Abstract: - In this paper, we generalize the result of Pant and Pant for a pair of mappings satisfying non-expansive or lipschitz type mapping pairs even without assuming continuity of mappings involved or completeness of the space by using R-weakly commuting type(Ag), introduced by Pathak et al.
Key words : non-expansive or lipschitz type mapping, R-weakly commuting type(Ag) Subject classification: (2001) 47 H10, 54H 25.
Reliability
analysis of a single unit and two protection device system with two types
of failure
Praveen Gupta and Manoj Saxena
Abstract: - This paper considers a single unit system
and two protection devices. Initially, the unit and protection devices
are in good condition. The system can fail by two types of failure (i)
Wearout failure and (ii) Castastrophic failure, subject to a single repair
facility with exponential failure time and arbitrary repair time distribution.
Using regenerative point technique in Markov renewal process, several
measures of reliability are obtained.
Simultaneous
dual integral equations with G-functions as kernels
Sudhir Singh*, S.K. Sharma** and Vinod Kumar***
Abstract: - In this paper, we deal with the formal solution
of simultaneous dual integral equations involving G-functions of two variables
as kernel by the method of fractional integration operators.
Exact Null Distribution of LRC for Testing Homogeneity of Completely Symmetric Gaussian Models
VIPIN TAYAL
Abstract: - In this paper exact null distributions of LRC for testing homogeneity of
completely symmetric Gaussian models are obtained in G and H-functions. The method of inverse Mellin transform is used to obtain densities. Key words and phrases: Null moments, inverse Mellin transform, Gauss-Legendre multiplication formula, G-function, H-function, Distributions.
Covering Properties, Semi Regular Properties, and Extremely Disconnectedness
Charles Dorsett
Abstract: - In this paper numerous covering properties are further investigated and each of semi regular properties and extremely disconnectedness are further examined.
Fixed Pint Theorem for Mapping Satisfying a General Contractive Condition of Integral Type in D-metric Space
Ramesh Kumar Vats, Renu Chugh* and Ramesh Kumar Vats**
Abstract: - In this paper, we analysis the existence of fixed point for a mapping defined on a complete D-metric space satisfying a general contractive condition of integral type.
Kew words : Fixed point, D-metric space.
Subject classification : (2001) AMS: 47H10, 54H25.
Construction
of Spaces with Unique Limit Point Using Filters
A. K. Desai and N. P. Shrimali
Abstract: - In this short communication, we indicate
a construction of a countable, topological space with exactly one limit
point. We define filters on N and use them to construct spaces of the
above mentioned type. These spaces are shown to be nonhomeomorphic. We
establish this using only the set-theoretic arguments.
AMS (2000) MATHEMATICS SUBJECT CLASSIFICATION 54A20, 54D80
Key words and phrases: Filter, Countable, Countable spaces
with unique limit point.